2 Answers
2

Perhaps you can parametrize your polygon and use ParametricPlot3D which takes MeshFunctions / MeshShading options. Alternately you could try interpolating your data and using ListSurfacePlot3D which also takes these options.

I commented out some of the options, because they made it difficult for me to see what was exactly happening. [Edit: Change the texture pattern to a variable, to clarify how to modify it. A line pattern given at end.]

If you have arbitrary polygons, then I don't know how to make the computation of VertexTextureCoordinateseasily automatic. (One could compute a projection rather automatically I suppose.) @Mr.Wizard's answer might be easiest in that case.

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